A generalized finite-difference time-domain scheme for solving nonlinear Schrodinger equations

被引：23

作者：

Moxley, Frederick Ira, III ^{[1
]}

Chuss, David T. ^{[2
]}

Dai, Weizhong ^{[1
]}

机构：

[1] Louisiana Tech Univ, Coll Engn & Sci, Ruston, LA 71272 USA

[2] NASA, Goddard Space Flight Ctr, Greenbelt, MD 20771 USA

来源：

COMPUTER PHYSICS COMMUNICATIONS | 2013年 / 184卷 / 08期

关键词：

Finite-difference time-domain (FDTD) scheme; Nonlinear Schrodinger equation; Soliton; DISCRETIZATION METHOD QDM; WAVES;

D O I：

10.1016/j.cpc.2013.03.006

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Recently, we have developed a generalized finite-difference time-domain (G-FDTD) method for solving the time dependent linear Schrodinger equation. The G-FDTD is explicit and permits an accurate solution with simple computation, and also relaxes the stability condition as compared with the original FDTD scheme. In this article, we extend the G-FDTD scheme to solve nonlinear Schrodinger equations. Using the discrete energy method, the G-FDTD scheme is shown to satisfy a discrete analogous form of the conservation law. The obtained scheme is tested by three examples of soliton propagation, including bright and dark solitons as well as a 2D case. Compared with other popular existing methods, numerical results show that the present scheme provides a more accurate solution. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：1834 / 1841

页数：8

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